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Chapter 5 Linear Inequalities and Linear Programming Section R Review

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2 Barnett/Ziegler/Byleen Finite Mathematics 12e Chapter 5 Review Important Terms, Symbols, Concepts 5.1 Inequalities in Two Variables A line divides the plane into two regions called half planes. A vertical line divides the plane into left and right half planes A nonvertical line divides it into upper and lower half planes. In either case, the dividing line is called the boundary line of each half-plane.

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3 Barnett/Ziegler/Byleen Finite Mathematics 12e Chapter 5 Review 5.1 Inequalities in Two Variables (continued) The graph of a linear inequality is the half plane obtained by following the procedure in this section. The variables in an applied problem are often required to be nonnegative.

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4 Barnett/Ziegler/Byleen Finite Mathematics 12e Chapter 5 Review 5.2 Systems of Linear Inequalities in Two Variables The solution region (also called the feasible region) of a system of linear inequalities is the graph of all ordered pairs that simultaneously satisfy all the inequalities in the system. A corner point of a solution region is a point in the region that is the intersection of two boundary lines. A solution region is bounded if it can be enclosed in a circle and unbounded if it can not.

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5 Barnett/Ziegler/Byleen Finite Mathematics 12e Chapter 5 Review 5.3 Linear Programming in Two Dimensions: Geometric Approach The problem of finding the optimal (maximum or minimum) value of a linear objective function on a feasible region is called a linear programming problem. The optimal value (if it exists) of the objective function in a linear programming problem must occur at one (or more) of the corner points of the feasible region. Existence criteria are described and a solution procedure is listed in this section.

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